在△ABC中，AB=2，AC=4，若点D为边BC的中点，P为△ABC的外心，给出下列数量积：①
题型： 填空题 难度： 一般
在△ABC中，AB=2，AC=4，若点D为边BC的中点，P为△ABC的外心，给出下列数量积：
①
|
|
| AB |
|
|
| AC |
②
|
|
| AD |
|
|
| BC |
③
|
|
| AD |
|
|
| AB |
④
|
|
| AP |
|
|
| AB |
⑤
|
|
| AP |
|
|
| BC |
其中其中数量积为定值的序号是______．（请填上所有正确的结论的序号）．
答案
①∵
|
|
| AB |
|
|
| AC |
②
|
|
| AD |
|
|
| BC |
| 1 |
| 2 |
|
|
| AB |
|
|
| AC |
|
|
| AC |
|
|
| AB |
| 1 |
| 2 |
③
|
|
| AD |
|
|
| AB |
| 1 |
| 2 |
|
|
| AB |
|
|
| AC |
|
|
| AB |
| 1 |
| 2 |
|
|
| AB |
|
|
| AC |
④
|
|
| AP |
|
|
| AB |
|
|
| AP |
|
|
| AB |
|
|
| AP |
|
|
| AB |
⑤
|
|
| AP |
|
|
| BC |
|
|
| AP |
|
|
| AC |
|
|
| AB |
|
|
| AP |
|
|
| AC |
|
|
| AP |
|
|
| AB |
综上，正确的结论的序号②④⑤
故答案为②④⑤
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